Mathematics Tes...

The mean of 20 observations is \(15 .\) On checking, it was found that two observations were wrongly copied as 3 and 6 . If wrong observations are replaced by correct values 8 and 4 , then the correct mean is:

What is the derivative of \(\sqrt{\frac{1+\cos x}{1-\cos x}}\)?

Find how many four letter word can be formed out of the word “PINEAPPLES”?

The system of equations:

\(2 x+y-3 z=5\)

\(3 x-2 y+2 z=5\) and

\(5 x-3 y-z=16\)

In a survey, it was found that \(21\) people liked product \(A, 26\) liked product \(B\) and \(29\) liked product \(C\). If \(14\) people liked products \(A\) and \(B\), \(12\) people liked products \(C\) and \(A, 14\) people liked products \(B\) and \(C\) and \(8\) liked all the three products. Find how many liked product \(C\) only.

\(\frac{\sin 7 x+6 \sin 5 x+17 \sin 3 x+12 \sin x}{\sin 6 x+5 \sin 4 x+12 \sin 2 x}\) equals:

What is the area of the region bounded by the parabolas y² = 6 (x - 1) and y² = 3x?

Axis of a parabola lies along x-axis. If its vertex and focus are at distances \(2\) and \(4\) respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

A fair coin tossed repeatedly. If the head appears on the first three tosses, then the probability of the tail appearing on the fourth toss equals.

Let \(f: \mathbf{R} \rightarrow \mathbf{R}\) be defined as \(f(x)=x^{4}\). Choose the correct answer.